计算机视觉研究的一个主要目的是从二维图像恢复三维物体的几何结构。为实现这一目的，通常需要图像匹配、摄像机标定和三维结构计算三个步骤，其中摄像机标定是不可或缺的一步。而图像间的极几何贯穿于上述三个步骤，并且在每一步都具有重要的作用，在有些情况下甚至是唯一可用的约束。因而极几何估计以及摄像机标定具有重要的理论意义和巨大的实用价值。本文围绕这两方面的问题开展了比较深入的研究。论文的主要工作如下： 1．汇聚点（the focus of expansion, 简称为FOE）的估计。提出了一种与经典几何估计方法等价的简化几何估计方法，大大降低了计算复杂性。另外，发现经典几何方法“校正”的图像对应点虽然满足极几何约束，但不满足内在的交比约束。在此基础上提出了一种新的几何方法，称为基于内在约束的几何方法，该方法可以得到更精确的FOE以及更可信的对应点。 2．三焦张量的因子化估计算法。现有的线性估计算法的测量矩阵元素通常是测量数据的非线性函数,这会放大测量误差,因子化算法可以克服该缺点。在给出三焦张量测量矩阵的因子分解的基础上，提出三焦张量的因子化估计算法,并给出了中间变量的几何意义和算法的代数残差。考虑到因子化算法扩展的解空间有可能导致不稳定的解,同时还提出了一种实用的因子化算法。 3．基于一维标定物的多摄像机标定算法。利用1D标定物标定摄像机通常需要限定其做一些特殊的运动。本文工作表明：当多个摄像机同时观察作任意刚体运动的1D标定物时，可以标定摄像机的内外参数。同时给出了基于分层重建的标定算法和基于无穷远单应矩阵的标定算法。对于多个摄像机构成的摄像机组，1D标定物不存在自身遮挡并且可以做任意刚体运动，与其他方法相比该方法更方便可行。
英文摘要
3D reconstruction from 2D images is one of the fundamental goals of computer vision. To fulfill the goal generally needs three steps: feature matching, camera calibration and 3D information processing. Camera calibration is an indispensable step for 3D reconstruction. Epipolar geometry plays an important role in each step of 3D reconstruction and is the unique available constraint in some cases. Thus, epipolar geometry estimation and camera calibration are very important in theory and practice. This study is focused on the two topics. The main work is summarized as follows: 1. FOE estimation. A simplified geometric method for FOE estimation, which is equivalent to classical geometric method, is proposed. The “corrected” corresponding pairs obtained by classical and simplified geometric method can’t meet some inherent cross ratio constraints. A new geometric algorithm which enforces the inherent constraints is also proposed, by which a better FOE and more faithful “corrected” corresponding pairs can be obtained. 2. Factorized algorithm for trifocal tensor estimation. The shortcoming of existing linear algorithms is that the element of measurement matrix is generally a nonlinear function of measurement data, which will amplify errors. To overcome this deficiency, a factorized algorithm for trifocal tensor estimation is proposed. The residual error and the geometric meaning of introduced variables in proposed algorithm are analyzed. A practical algorithm is also proposed to ensure a robust solution. 3. Multi-camera calibration with 1D object. It is well known that it is impossible to calibrate a single camera if the 1D object’s motion is of general one. For a multi-camera setup, can the cameras be calibrated by a 1D object undergoing general motion? It is proved that each one of multi-camera can be calibrated with 1D calibration object. And two calibration algorithms based on stratified reconstruction and infinite homography are proposed. There’s no self-occlusion for 1D object undergoing general motions, therefore the proposed algorithm more feasible and practical.
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